Evaluations of Noncommutative Polynomials on Algebras: Methods and Problems, and the L'vov-Kaplansky Conjecture

• Published in: Symmetry, Integrability and Geometry: Methods and Applications
• Date: 2020
• Main Authors: Kanel-Belov, Alexei, Malev, Sergey, Rowen, Louis, Yavich, Roman
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2020
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/210777
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: Evaluations of Noncommutative Polynomials on Algebras: Methods and Problems, and the L'vov-Kaplansky Conjecture. Alexei Kanel-Belov, Sergey Malev, Louis Rowen and Roman Yavich. SIGMA 16 (2020), 071, 61 pages

Let be a polynomial in several non-commuting variables with coefficients in a field of arbitrary characteristic. It has been conjectured that for any , for multilinear, the image of evaluated on the set Mₙ() of by matrices is either zero, or the set of scalar matrices, or the set slₙ() of matr...